Open Quantum Systems
Open Quantum Systems
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DOI：
10.29172/37d54ed9-50d7-491e-a874-5adb42615c2b
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发表时间：
2021-12
期刊：
影响因子：
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通讯作者：
Frederik Nathan;M. Rudner
中科院分区：
文献类型：
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作者：
Frederik Nathan;M. Rudner
我们开发了一个新的马尔可夫主方程的Lindblad形式，使有效的研究范围广泛的量子少体和多体系统耦合到外部浴。主方程的有效性完全基于浴和系统-浴耦合的性质，而对系统本身内的能级结构没有任何要求。主方程推导使用马尔可夫近似，这是不同于早期的方法中使用的。我们提供了一个严格的约束，由这个马尔可夫近似引起的误差，误差是由一个无量纲的组合的内在相关性和松弛时间尺度的浴控制。我们的主方程在与布洛赫-红场方程相同的近似水平上是精确的。与布洛赫-红场方法相比，我们的方法确保了密度矩阵的正性。因此，我们的方法是鲁棒的，并且可以有效地使用纯态（而不是密度矩阵）的随机演化来求解。我们讨论了如何将我们的方法应用于静态或驱动量子多体系统，并通过数值模拟的自旋链，这将是具有挑战性的治疗现有的方法来说明它的力量。
We develop a novel Markovian master equation in the Lindblad form that enables the efficient study of a wide range of quantum few-and many-body systems coupled to external baths. The validity of the master equation is based entirely on properties of the bath and the system-bath coupling, without any requirements on the level structure within the system itself. The master equation is derived using a Markov approximation that is distinct from that used in earlier approaches. We provide a rigorous bound for the error induced by this Markov approximation; the error is controlled by a dimensionless combination of intrinsic correlation and relaxation timescales of the bath. Our master equation is accurate on the same level of approximation as the Bloch-Redfield equation. In contrast to the Bloch-Redfield approach, our approach ensures preservation of the positivity of the density matrix. As a result, our method is robust, and can be solved efficiently using stochastic evolution of pure states (rather than density matrices). We discuss how our method can be applied to static or driven quantum many-body systems, and illustrate its power through numerical simulation of a spin chain that would be challenging to treat by existing methods.